ECAT Math MCQs with Answers

All ECAT tests in Pakistan for pre-engineering and ICS students have a math section. ECAT math tests are MCQ based exams that derive from the intermediate curriculum. Details of ECAT math topics are given in the next section.

Additionally, some exams like the FAST university entry test or the NTS NAT for COMSATS also have a basic math or quantitative reasoning section, which test students’ basic math, problem solving and critical thinking skills. In some tests, the math section is the largest and has the most weightage. For instance, in the NUST entry Test (NET), the math section is worth 40% and consists of 80 questions. For more details on which universities accept ECAT, click here. And for various test patterns, visit this link.

This article will go into detail about ECAT math MCQs, ECAT math syllabus, ECAT math shortcuts, ECAT math tricks, ECAT math notes, and also give you some ECAT math MCQs with answers.

ECAT Math Test Syllabus
ECAT Math MCQs with Answers
ECAT Math Shortcuts and Math Tricks for ECAT
How to Prepare for ECAT Math Test
Answer Key to the ECAT Math Test
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ECAT Math Test Syllabus

Math ECAT MCQs are usually derived from the intermediate or adjacent curriculums. They test students’ knowledge and skills in topics of algebra, trigonometry, calculus and analytic geometry. While all these topics should be familiar to student having studied mathematics in intermediate or A levels, the format of these tests and the question type can be new to them. This is why learning ECAT math tricks and shortcuts is very important.

Number Systems
Matrices and Determinants
Quadratic Equations
Partial Fractions
Sequences and Series
Permutation and Combination
Probability
Mathematical Induction and Binomial Theorem
Fundamentals of Trigonometry
Trigonometric Identities
Solutions of Triangles
Trigonometric Graphs and Inverses
Trigonometric Equations
Functions and Limits
Differentiation
Integration
Analytic Geometry and Straight Lines
Circles, Ellipses, Parabolas and Hyperbolas
Linear Inequalities and Linear Programming
Vectors
Exponents and Logarithms

In addition to these, some tests have a basic math or quantitative reasoning section. These sections contain word problems to test students’ comprehension, critical thinking and problem solving skills and are generally from topics of arithmetic, algebra, and geometry.

Topics that are tested could include (but are not limited to):

Averages and Weighted Averages
Fractions
Ratio and Proportion
Work
Speed, Time, and Distance
Percentages
Selling Price, Cost, and Profit
Simple and Compound Interest

This section contains an ECAT math test, with MCQs from ECAT math past papers. This will serve not only as a good source for sample questions but also as an ECAT math mock test to check your preparation level. To help you gauge your skill level in various topics, topic and difficulty level for each question is also given.

Below is a list of sample ECAT math MCQs with answers.

The product of two complex conjugate numbers is
1. A real number
2. An imaginary number
3. Always zero
4. Not defined
  Topic: Number Systems
  Difficulty Level: Medium

If E = {months of the year}, F = {months with exactly 30 days }, G = {months with exactly 31 days}, then which one of the following is correct?
1. G ⊆ F
2. F ⊆ G
3. G ⊂ E
4. E ⊆ F
  Topic: Sets and Functions
  Difficulty Level: Easy

If any two columns of a square matrix A are interchanged then |A| =?
1. 0
2. 1
3. Multiplicative inverse of the determinant of the original matrix
4. Additive inverse of the determinant of the original matrix
  Topics: Matrices and Determinants
  Difficulty Level: Easy

If discriminant is positive and perfect square, then roots are
1. Real and equal
2. Imaginary and distinct
3. Real, rational and distinct
4. Real, irrational and distinct
  Topic: Quadratic Equations
  Difficulty: Medium

How many partial fractions will there be in the expansion of the above fraction:
1. 1
2. 2
3. 3
4. 4
  Topic: Partial Fractions
  Difficulty Level: Medium

What is the sum of series 1+4+16+……….. to 10 terms:
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Topic: Sequences and Series
Difficulty Level: Hard

These are the answer options for question 6

In how many ways can 3 English, 2 Urdu and 2 Math books be arranged on a shelf so as to keep all the books in each language together?
1. 144
2. 288
3. 72
4. 24
  Topic: Permutation and Combination
  Difficulty Level: Hard

A die is rolled once. Find the probability of getting a number > 4?
1. 2/3
2. 1
3. 1/3
4. 1/2
  Topic: Probability
  Difficulty Level: Medium

This is a binomial expression of degree 5

The coefficient of third term of the binomial expression given above is
1. 10
2. 20
3. 30
4. None of these
  Topic: Mathematical Induction and Binomial Theorem
  Difficulty Level: Medium

The square of the sum of sine of A and cosine of A

The above expression is equal to:
1. 1 + 2sinAcosA
2. 1 - 2sinAcosA
3. 2sinAcosA – 1
4. 2sinAcosA + 1
  Topic: Trigonometric Identities
  Difficulty Level: Medium

A slide should be built in a park that has to be set up at 10 meters height and also 10 meters away from the support. What should be the angle of elevation?
1. 30
2. 45
3. 60
4. 90
  Topic: Fundamentals of Trigonometry
  ‍Difficulty Level: Medium

If triangle of base 6 units has the same areas as a circle of radius 6 units. What is the altitude of the triangle?
1. 10π
2. 12π
3. 6π
4. None of these
  Topic: Solutions of Triangle
  Difficulty Level: Medium

This is a question involving functions and limits

For the functions given above, what is the limit of f(x) as x approaches a?
1. 1.5
2. 2
3. 0.5
4. 0.67
  Topic: Functions and Limits
  ‍Difficulty Level: Hard

If y=sin(2x+3) then the derivative of y with respecto x is:
1. 6cos(2x+3)
2. 2sec(2x+3)
3. 2cos(2x+3)
4. None of these
  Topic: Differentiation
  Difficulty Level: Medium

What is the definite integral of x from x = 0 to x = 1?
1. 0
2. 1/2
3. 2
4. 3
  Topic: Integration
  Difficulty Level: Easy

If two lines with slopes m and n are parallel, then
1. m=n
2. m+n=1
3. m-n=-1
4. mn=-1
  Topic: Analytic Geometry: Straight Lines
  Difficulty Level: Medium

In 2004, 200 workers received pays on hourly basis from 15 dollar per hour to 25 dollar per hour according to the difficulty of assigned tasks. The largest possible amount paid to the workers for 8 working hours is ___________.
1. $215
2. $165
3. $200
4. $170
  Topic: Linear Inequalities and Linear Programming
  Difficulty Level: Medium

All radii of a circle are
1. unique
2. congruent
3. imaginary
4. none of the above
  Topic: Circles
  Difficulty Level: Easy

This is a quadratic equation representing a parabola

What is the vertex of the parabola given above
1. (-3, 4)
2. (3, -4)
3. (3, 4)
4. (-3, -4)
  Topic: Parabola, Ellipse, Hyperbola
  Difficulty Level: Medium

The vector that must be added to the vector i-3j+2k and 3i+6j-7k so that the resultant vector is a unit vector along the y-axis is
1. 4i+2j+5k
2. -4i-2j+5k
3. 3i+4j+5k
4. Null vector
  Topic: Vectors
  Difficulty Level: Hard

You can find the answer key for these ECAT MCQs with answers at the end of this page.

For similar articles about other subjects, visit the following sites:

‍ECAT English MCQs‍

For another free ECAT diagnostic test, click here.

For more details on ECAT Past Papers, you can look though this article.

ECAT Math Shortcuts and Math Tricks for ECAT

Since most ECAT tests are MCQ based and have a strict and short time limit, students need to learn quick ways to solve these questions. There is no need to show your working as long as you arrive at the correct answers. Some tests also do not allow calculators so students need to brush on their mental math as well.

The first thing that need to do for mental math is memorize your times tables, the squares and square roots and cubes and cube roots of at least the first 20 natural numbers. Usually these arithmetic guides and important formulas are given in ECAT math notes.

This is a table of all squares and cubes of natural numbers up to 20

You should also memorize the trigonometric ratios for special angles. There’s a few tricks for easily remembering these, some are discussed in our video lectures. This is very useful for solving ECAT MCQs with answers.

You should also memorize all relevant ECAT math formulae. These will also be provided in Maqsad’s ECAT math notes to students to sign up to our batch.

There are also ECAT math shortcuts for solving questions related to matrices, quadratics, sequences, probability, calculus etc. All of these are discussed in our live classes and video lectures.

You can also make use of Test-Taking Strategies such as triaging the test, eliminating the wrong answers and guessing (if there is no negative marking!)

STRATEGY 1: TRIAGING THE TEST

You do not need to complete questions in order. To triage the test effectively, do the following:

First, work through all the easy questions you can do quickly. Skip the questions that are hard or time-consuming
Second, work through the questions that are doable but time-consuming
Third, work through the hard questions
If you run out of time, pick a Letter of the Day for remaining questions

A Letter of the Day is an answer choice letter (A, B, C, or D) that choose to select for questions you guess on.

STRATEGY 2: ELIMINATION

If you can determine that one or more answer choices are definitely incorrect, you can increase your chances of getting a right answer by paring the selection down. To eliminate answer choices, do the following:

Read each answer choice
Cross out the answer choices that are incorrect
Remember: there is no negative marking so take your best guess

STRATEGY 3: GUESSING

Each MCQ usually has four options and no negative marking (in some tests). That means if you have no idea how to approach a question, you have a 25 percent chance of choosing the correct answer. Even though there’s still a 75 percent chance of selecting an incorrect answer, you won’t lose any points for doing so. The worst that can happen is that you earn zero points on a question, which means you should always at least take a guess, even when you have no idea what to do. When guessing on a question do the following:

Always try to strategically eliminate answer choices before guessing
If you run out of time, or have no idea what a question is asking, pick a Letter of the Day.

How to Prepare for ECAT Math Test?

It is very important to dedicate time to prepare for ECAT tests. While the concepts may seem familiar, the format of questions and paper patterns are new to most students.

Start by giving a diagnostic test. This will tell you where you stand and which topics you need to focus on.
To revise your concepts and strengthen your understanding, use our detailed Video Lectures.
Attend live ECAT math classes online with expert teachers you can ask questions in real time.
The main component of your preparation is practice. For lots of topical practice and FLPs, you can use Maqsad’s tests.
To sign-up for Maqsad’s ECAT Batch 2025, click here!